The present invention relates to a digital phase ramp type fiber optic gyro in which light is propagated clockwise and counterclockwise through a loop-shaped optical transmission line, a ramp signal which provides a stepwise ramp phase which cancels a phase difference between the clockwise and counterclockwise light beams which is caused by an angular rate applied to the optical transmission line and a biasing signal which provides phase differences +.pi./2 rad and -.pi./2 rad alternately between the both light beams are produced and the input angular rate is detected, based on the step size or frequency of the ramp signal.
FIG. 1 schematically shows a conventional digital phase ramp type fiber optic gyro. A light beam emitted from a light source 11 such as a laser is split by a beam splitter 12 into two beams, which are supplied to both ends of a loop-shaped optical transmission line formed by, for example, a plane-of-polarization retaining optical fiber coil, and are propagated therethrough as clockwise and counterclockwise beams 14 and 15. The beams 14 and 15 thus propagated through the optical transmission line 13 and emitted therefrom are coupled again by the beam splitter 12 and interfere with each other. The resulting interference light is transduced by an opto-electric transducer 16 into an electric signal corresponding to the intensity of the interference light, and the electric signal is amplified by an AC amplifier 17. An optical phase modulator 18 is interposed between the beam splitter 12 and the optical transmission line 13.
Now, let the time necessary for the propagation of the light from the light source 11 through the optical transmission line 13 be represented by .tau.. A digital biasing signal generator 19 generates a digital biasing signal .phi..sub.B of such digital values that cause to add phase differences +.pi./2 rad and -.pi./2 rad alternately to a phase difference between the both light beams 14 and 15 when they are coupled or combined by the beam splitter 12, at time intervals of k.tau. (where k is a predetermined desired odd number, the following description being given of the case where k=1). In the following description the biasing phase differences +.pi./2 rad will also be indicated by the same reference notation .phi..sub.B as that used for the biasing signal. The output of the AC amplifier 17 is synchronously detected by a synchronous detector 22 using the biasing signal .phi..sub.B as a reference signal and the detected output is used to generate a digital step value .phi..sub.B by a step value generator 28. The digital biasing signal .phi..sub.B is added to the digital step value .phi..sub.s in an adder 32, and the added output is accumulated by an accumulator 33 at k.tau. time intervals. The accumulated output of the accumulator 33 is converted by a D/A converter 21 into an analog signal, which is applied to the optical phase modulator 18.
The relationship between the phase difference .DELTA..phi. between the both light beams 14 and 15 when they are coupled together and the output level I obtained by amplifying the transduced electric signal corresponding to the intensity of the interference light, by the AC amplifier 17 is such as indicated by the curve 23 in FIG. 2. With no angular rate being applied to the optical transmission line 13 around its axis, the phase difference .DELTA..phi. between the clockwise and counterclockwise light beams 14 and 15 varies about a zero phase by .pi./2 in positive and negative directions at k.tau. (k=1) time intervals owing to the modulation by the optical phase modulator 18, and the output level of the AC amplifier 17 becomes constant as indicated by the line 25, reducing the output of the synchronous detector 22 to zero.
When an angular rate is applied to the optical transmission line 13 around its axis, however, a phase difference .phi..sub.r (hereinafter referred to as a Sagnac phase shift) is introduced, by the Sagnac effect, between the clockwise and counterclockwise light beams 14 and 15 in accordance with the direction and magnitude of the input angular rate. Owing to the influence of the Sagnac phase shift .phi..sub.r the phase difference .DELTA..phi. between the light beams 14 and 15 varies about a phase displaced .phi..sub.r from the zero phase by the same amount in positive and negative directions at k.tau. time intervals as indicated by the curve 26. Consequently, the output level of the AC amplifier 17 at that time becomes a rectangular wave whose level goes up and down at k.tau. time intervals as indicated by the curve 27, and the rectangular wave becomes in phase or 180.degree. out of phase with the digital biasing signal .phi..sub.B of a 50% duty from the digital biasing signal generator 19, depending on the polarity of the Sagnac phase shift .phi..sub. r. Hence, the level and polarity of the detected output obtained by synchronously detecting the output of the AC amplifier 17 with the synchronous detector 22 correspond to the magnitude and direction of the input angular rate. The synchronously detected output is used by the step value generator 28 to produce a negative feedback signal (a step value signal) .phi..sub.s which will reduce the output of the synchronous detector 22 to zero. Thus, the output of the synchronous detector 22 is representative of a negative phase feedback error. The step value generator 28 comprises a PID (proportional plus integral plus derivative) filter or similar analog calculator 29 which is supplied with the output of the synchronous detector 22 and an A/D converter 31 which converts the output of the analog calculator 29 to a digital signal. In the state of equilibrium by the negative feedback of the step value signal .phi..sub.s the magnitude and direction of the input angular rate can be known from the value and polarity of the step value signal .phi..sub.s, because it has a magnitude and polarity by which the phase difference .phi..sub.r introduced between the clockwise and counterclockwise light beams 14 and 15 by the Sagnac effect can be cancelled. In the following description the step phase difference which is provided by the step value signal .phi..sub.s will also be identified by the same reference notation .phi..sub.B.
The step value .phi..sub.s such as shown in FIG. 3A and the digital biasing signal .phi..sub.B such as shown in FIG. 3B are added together by the adder 32 as mentioned above and the added output is accumulated by the accumulator 33 at the k.tau. time intervals. The accumulated output becomes as indicated by the solid line in FIG. 3C. The output of the accumulator 33 is converted by a D/A converter 21 to an analog value, which is applied as a modulation signal to the optical phase modulator 18.
The phase shifts of the clockwise and counterclockwise light beams 14 and 15 having returned to the beam splitter 12, caused by the optical phase modulator 18, are such as indicated by the solid line and the broken line in FIG. 3C, since the clockwise light beam 14 lags the beam 15 by the propagation time .tau.. Consequently, the phase difference .DELTA..phi. between the both beams 14 and 15 is the sum of the step value signal .phi..sub.s and the biasing signal .phi..sub.B as shown in FIG. 3D. Hence, by controlling the step value .phi..sub.s so that the output of the synchronous detector 22 may be reduced to zero, the step value .phi..sub.s will become equal to the Sagnac phase shift .phi..sub.r caused by the input angular rate. The Sagnac phase shift .phi..sub.r is expressed by the following equation: EQU .phi..sub.r =4.pi.RL.OMEGA./(.lambda.C) (1)
where R is the radius of the optical transmission line 13, L the length of the optical transmission line (an optical fiber) 13, .lambda. is the wavelength of emitted light from the light source 11, C is the velocity of light in a vacuum and .OMEGA. is the input angular rate.
Therefore, EQU .OMEGA.=.phi..sub.r .multidot..lambda.C/(4.pi.RL)=.phi..sub.s .lambda.C/(4.pi.RL) (2)
By obtaining the step value .phi..sub.s based on the relationship between the electric signal applied to the optical phase modulator 18 and the resulting phase shift amount and substituting the step value into Eq. (2), the input angular rate .OMEGA. can be obtained.
In practice, however, it is convenient to obtain the input angular rate .OMEGA. in such a manner as mentioned below. The accumulator 33 outputs an overflow value as its accumulated value when the absolute value of the accumulated value is in excess of a predetermined threshold value corresponding to 2m.pi. rad (where m is usually a positive integer, and FIGS. 3C and 3D show the case where m=1). Letting the number of accumulations between an overflow and the next overflow and the period of the overflow be represented by p and T, respectively, EQU .phi..sub.s =2m.pi./p, p=T/.tau.
because of the following relationships: EQU p.phi..sub.s =2m.pi., p.pi.=T.ident.1/f.
Hence, EQU .phi..sub.s =2m.pi..tau./T=2m.pi..tau.f (3)
Substitution of Eq. (3) into Eq. (2) gives EQU .OMEGA.=.lambda.C.multidot.m.tau.f/2RL (4)
Since .tau.=nL/C (where n is the refractive index of the optical transmission line 13), its substitution into Eq. (4) gives EQU .OMEGA.=.lambda.n.multidot.mf/2R (5)
By measuring the frequency f of the overflow of the accumulator 33, the input angular rate .OMEGA. can be obtained. In the case where the digital biasing signal .phi..sub.B corresponding to .+-..pi./2 is not applied to the adder 32, the output of the accumulator 33 varies stepwise in the positive or negative direction depending on the polarity of the step value signal .phi..sub.s in the intervals of overflows; hence, the output of the accumulator 33 will hereinafter be referred to as a positive or negative digital ramp signal.
If the input angular rate is not so large as to cause a phase shift .phi..sub.r =.phi..sub.s in excess of .+-..pi./2 rad (i.e. if .vertline..phi..sub.s .vertline.&lt;.pi./2), an overflow occurs when the step value .phi..sub.s is positive and the biasing signal .phi..sub.B is +.pi./2 rad as indicated by an arrow OVF in FIG. 4A or when the step value .phi..sub.s is negative and the biasing signal .phi..sub.B is -.pi./2 rad as shown in FIG. 4B. In this instance, the phase difference .DELTA..phi. becomes .+-.(2m.pi.-.pi./2)+.phi..sub.s. In the steady state of the negative feedback operation, since the step value .phi..sub.s is cancelled by the Sagnac phase shift .phi..sub.r, the intensity of interference light which is observed in the opto-electric transducer 16 is the intensity at positions where the phase difference .DELTA..phi. between the both light beams 14 and 15 is .+-.(.+-.( 2m.pi.-.pi./2 rad). Setting m=1, the phase difference .+-.3.pi./2, which correspond to operation points C and D in FIG. 5. The phase differences .DELTA..phi. when no overflow occurs are .+-..pi./2 which correspond to operation points A and B. In short, in the steady state of the negative feedback operation the intensity of interference light which is observed in opto-electric transducer 16 is constant, ideally, irrespective of the occurrence of an overflow.
The threshold value of the accumulator 33 is set to correspond to the phase shift amount 2m.pi. rad by the optical phase modulator 18 as referred to previously, but the conversion gain of the optical phase modulator 18 varies with temperature and similar ambient conditions. In consequence, the phase shift amount by the optical phase modulator 18, corresponding to the threshold value of the accumulator 33, deviates from the above-mentioned value 2m.pi. rad. Since this deviation is equivalent to a deviation of the value of m from its integral value, the exact input angular rate .OMEGA. cannot be measured as will be seen from Eq. (5), for instance.
In the case where the conversion gain of the optical phase modulator 18 has become smaller than its initial value and in the state in which the Sagnac phase shift .phi..sub.r and the step value .phi..sub.s are cancelled each other, the absolute value of the phase difference between the both light beams 14 and 15 immediately after an overflow is smaller than (2m.pi.-.pi./2) rad, and the interference light intensity detected by the opto-electric transducer 16 moves because of the overflow from the operation point A (or B) not to the operation point C (or D) but to the operation point E (or F) in FIG. 5 which is lower than the intensity at the operation point A (or B). Similarly, in the case where the conversion gain of the optical phase modulator 18 has become greater than its initial value and in the state where the Sagnac phase shift .phi..sub.r and the step value .phi..sub.s are cancelled each other,
the absolute value of the phase difference .DELTA..phi. between the both light beams 14 and 15 immediately after an overflow becomes larger than (2m.pi.-.pi./2) rad, and the intensity of the interference light which is observed in the opto-electric transducer 16 moves from the operation point A (or B) to the operation point G (or H), higher than the intensity at the operation point A (or B).
A conversion gain controller 35 compares, through utilization of such phenomena, output levels of the AC amplifier 17 is respective periods .tau. before and after the overflow and controls the conversion gain of the D/A converter 21 to increase or decrease, depending on whether the output after the overflow is smaller or larger than the output before the overflow. In this way, the conversion gain of the D/A converter 21 is corrected so that the threshold value of the accumulator 33 may always correspond to the phase shift amount 2m.pi. rad by the optical phase modulator 18. The conversion gain of the D/A converter 21 can be corrected by using a multiplying type D/A converter and applying thereto the output of the conversion gain controller 35 as a multiplication signal.
In the above-described digital phase ramp type fiber optic gyro, when a large angular rate which will cause a phase shift greater than .pi./2 rad in absolute value is input thereinto, an overflow occurs when the ramp signal is positive and the biasing signal .phi..sub.B is -.pi./2 (or when the ramp signal is negative and the biasing signal .phi..sub.B is +.pi./2 and the operation point may sometimes jump from B (or A) to J (or I) where the phase difference .DELTA..phi. between the clockwise and counterclockwise light beams 14 and 15 is -5.pi./2 (or +5.pi./2) In other words, when an overflow occurs, the phase difference .DELTA..phi. may sometimes becomes .+-.(2m.pi.+.pi./2) rad, in general.
In this case, if the conversion gain of the optical phase modulator 18 becomes smaller than its initial value, the absolute value of the phase difference .DELTA..phi. immediately after the overflow becomes smaller than (2m.pi.+.pi./2) rad and the intensity of the interference light which is observed in the opto-electric transducer 16 is the intensity at the operation point L (or K), higher than the intensity of the interference light at the operation point B (or A). As a result, the output after the overflow becomes larger than the output before the overflow. If the conversion gain of the D/A converter 21 is reduced by the conventional method, then the feedback will become positive, resulting in the absolute value of the phase difference immediately after the overflow becoming further smaller than (2m.pi.+.pi./2) rad.
Conversely, when the conversion gain of the optical phase modulator 18 has become larger than its initial value, the absolute value of the phase difference .DELTA..phi. between the both light beams 14 and 15 immediately after the overflow becomes greater than (2m.pi.+.pi./2) rad and the intensity of the interference light which is observed in the opto-electric transducer 16 becomes the intensity at the operation point N (or M), lower than the intensity at the operation point B (or A). That is, the output after the overflow becomes smaller than the output before the overflow, increasing the conversion gain of the D/A converter 21. Consequently, a positive feedback takes place and the absolute value of the phase difference .DELTA..phi. during the overflow becomes further greater than (2m.pi.+.pi./2) rad.
Generally speaking, when an input angular rate which causes a phase shift greater than .pi./2 rad in absolute value is input, the phase difference .DELTA..phi. between the both light beams 14 and 15 immediately after the overflow may sometimes assume values of not only .+-.(2m.pi.-.pi./2) rad but also .+-.(2m.pi.+.pi./2) rad in the state of the Sagnac phase shift amount .phi..sub.r and the step value .phi..sub.s being cancelled each other, and in the latter case the correction control for a change in the conversion gain of the optical phase modulator 18 becomes a positive feedback, making it impossible to correctly detect the angular rate.
Also in the case where the optical phase modulation by the digital ramp signal and the optical phase modulation by the biasing signal are carried out independently of each other through use of individual optical phase modulators, the phase difference between the both light beams during an overflow may sometimes assume the values of .+-.(2m.pi.+.pi./2) rad as well as .+-.(2m.pi.-.pi./2) rad in the state of the Sagnac phase shift amount .phi..sub.r and the step value .phi..sub.s being cancelled each other, and in the former case the correction control for a change in the conversion gain of the optical phase modulator 18 cannot be achieved as is the case with the above.